Given the electric flux density determine

(a) pv by applying Eq. (4.26),
(b) The total charge Q...

Question

Given the electric flux density determine
  
(a) pv by applying Eq. (4.26),
(b) The total charge Q enclosed in a cube 2 m on a side, located in the first octant with three of its sides coincident with the x-, y-, and z-axes and one of its corners at the origin, and
(c) The total charge Q in the cube, obtained by applying Eq. (4.29).

Robert · Accepted Answer

Manual2009.dvi
x2(x+ y)+ ŷ(3x−2y) (C/m2)
determine
(a) ρv by applying Eq. (4.26).
(b) The total charge Q enclosed in a cube 2 m on a side, located in the first octant
with three of its sides coincident with the x-, y-, and z-axes and one of its
corners at the origin.
(c) The total charge Q in the cube, obtained by applying Eq. (4.29).
Solution:
(a) By applying Eq. (4.26)
ρv = ∇ ·D=
∂
∂x
(2x+2y)+
∂
∂y
(3x−2y) = 0.
(b) Integrate the charge density over the volume as in Eq. (4.27):
Q=
∫
V
∇ ·D dV =
∫ 2
x=0
∫ 2
y=0
∫ 2
z=0
0 dx dy dz= 0.

Given the electric flux density determine (a) pv by applying Eq. (4.26), (b) The total charge Q enclosed in a cube 2 m on a side, located in the first octant with three of its sides coincident with...

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